A366180 - OEIS

%I #9 Oct 03 2023 09:00:12

%S 1,3,15,109,909,8184,77626,764226,7735878,80011063,841875232,

%T 8983175079,96977392945,1057262750608,11623867926024,128730566729686,

%U 1434752590885174,16080839356274157,181135636330594960,2049430159361529977,23280997677471432102

%N G.f. A(x) satisfies A(x) = 1/(1 - x)^2 + x*A(x)^3/(1 - x)^3.

%F a(n) = Sum_{k=0..n} binomial(n+6*k+1,n-k) * binomial(3*k,k)/(2*k+1).

%o (PARI) a(n) = sum(k=0, n, binomial(n+6*k+1, n-k)*binomial(3*k, k)/(2*k+1));

%Y Partial sums give A366182.

%Y Cf. A364620, A364629, A366179.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 03 2023